Note on the Erdos-Szekeres theorem

被引：35
|
作者：
Toth, G
Valtr, P
机构：
[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA
[2] Rutgers State Univ, DIMACS Ctr, Piscataway, NJ 08855 USA
[3] Charles Univ, Dept Appl Math, CR-11800 Prague, Czech Republic
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 1998年 / 19卷 / 03期
关键词：
General Position; Convex Position; Szekeres Theorem;
D O I：
10.1007/PL00009363
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Let g(n) denote the least integer such that among any g(n) points in general position in the plane there are always n in convex position. In 1935, P. Erdos and G. Szekeres showed that g(n) exists and [GRAPHICS] Recently, the upper bounds has been slightly improved by Chung and Graham and by Kleitman and Pachter. In this paper we further improve the upper bound to [GRAPHICS]
引用
收藏
页码：457 / 459
页数：3
相关论文
共 50 条
  • [41] On the Erdos-Szekeres n-interior-point problem
    Bharadwaj, B. V. Subramanya
    Govindarajan, Sathish
    Sharma, Karmveer
    EUROPEAN JOURNAL OF COMBINATORICS, 2014, 35 : 86 - 94
  • [42] The Erdos-Szekeres problem on points in convex position - A survey
    Morris, W
    Soltan, V
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 37 (04) : 437 - 458
  • [43] Two Upper Bounds for the Erdos-Szekeres Number with Conditions
    Strunk, Florian
    DISCRETE & COMPUTATIONAL GEOMETRY, 2013, 49 (02) : 183 - 188
  • [44] On the generalized Erdos-Szekeres conjecture a new upper bound
    Caro, Y
    DISCRETE MATHEMATICS, 1996, 160 (1-3) : 229 - 233
  • [45] AVERAGE GROWTH OF Lp NORMS OF ERDOS-SZEKERES POLYNOMIALS
    Billsborough, C.
    Gold, S.
    Linder, E.
    Lubinsky, D. S.
    Yu, J.
    ACTA MATHEMATICA HUNGARICA, 2022, 166 (01) : 179 - 204
  • [46] Erdos-Szekeres "happy end"-type theorems for separoids
    Strausz, Ricardo
    EUROPEAN JOURNAL OF COMBINATORICS, 2008, 29 (04) : 1076 - 1085
  • [47] Two player game variant of the Erdos-Szekeres problem
    Kolipaka, Parikshit
    Govindarajan, Sathish
    DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2013, 15 (03): : 73 - 100
  • [48] Computer solution to the 17-point Erdos-Szekeres problem
    Szekeres, George
    Peters, Lindsay
    ANZIAM JOURNAL, 2006, 48 : 151 - 164
  • [49] THE ERDOS-SZEKERES PROBLEM FOR NON-CROSSING CONVEX SETS
    Dobbins, Michael Gene
    Holmsen, Andreas
    Hubard, Alfredo
    MATHEMATIKA, 2014, 60 (02) : 463 - 484
  • [50] A Positive Fraction Erdos - Szekeres Theorem
    I. Bárány
    Discrete & Computational Geometry, 1998, 19 : 335 - 342
12345